EVENT DETAILS AND ABSTRACT

Title: Maximum principles in self-similar potential flow
Speaker: Professor Volker Elling
Speaker Info: Stanford University
Brief Description:
Special Note:
Abstract:

Motivated by inaccuracy and documented failures of numerical approximations and by a general lack of theoretical insight, research has begun on constructing exact solutions of PDE that model compressible fluids. The potential flow equation is suitable in situations with negligible friction, heat conduction and vorticity. Self-similar solutions arise as large-time asymptotes of general solutions and as exact solutions of many important special cases. Self-similar potential flow is a quasilinear second-order PDE of mixed type. Towards constructing exact solutions it is necessary to identify elliptic and hyperbolic regions and to develop perturbation methods and a priori estimates. To this end we proved a strict maximum principle for the local pseudo-Mach number which determines the local type. The result shows that elliptic region must stay elliptic under perturbations of parabolic boundaries. We also discuss maximum and minimum principles for density and other physical quantities.